We use APOGEE DR13 data to examine the metallicity trends in the Milky Way (MW) bulge and we explore their origin by comparing two N-body models of isolated galaxies that develop a bar and a boxy/peanut (b/p) bulge. Both models have been proposed as scenarios for reconciling a disc origin of the MW bulge with a negative vertical metallicity gradient. The first model is a superposition of cospatial, i.e. overlapping, disc populations with different scale heights, kinematics, and metallicities. In this model the thick, metal-poor, and centrally concentrated disc populations contribute significantly to the stellar mass budget in the inner galaxy. The second model is a single disc with an initial steep radial metallicity gradient; this disc is mapped by the bar into the b/p bulge in such a way that the vertical metallicity gradient of the MW bulge is reproduced, as has been shown already in previous works in the literature. However, as we show here, the latter model does not reproduce the positive longitudinal metallicity gradient of the inner disc, nor the metalpoor innermost regions seen in the data. On the other hand, the model with co-spatial thin and thick disc populations reproduces all the aforementioned trends. We therefore see that it is possible to reconcile a (primarily) disc origin for the MW bulge with the observed trends in metallicity by mapping the inner thin and thick discs of the MW into a b/p. For this scenario to reproduce the observations, the α-enhanced, metal-poor, thick disc populations must have a significant mass contribution in the inner regions, as has been suggested for the Milky Way.